Seismic Analysis of Indoor Auditorium S.Dilipan Bose *, S

International Journal of Scientific & Engineering Research, Volume 5, Issue 4, April-2014 1123 ISSN 2229-5518 Seismic Analysis of Indoor Auditorium S.Dilipan Bose *, S. Aravindan# *PG Student M.tech Structural Engineering, Bharath University. # Assistant Professor, Department of Civil Engineering, Bharath University.

Abstract— The project titled “Seismic analysis of Indoor Auditorium” has been taken up with an objective to determine the seismic response and behaviour of an Auditorium constructed in Chennai area. Even though Chennai is considered as least prone to major earthquake, it is expected that a structure would survive major earthquakes without collapse that might occur unexpectedly during the life of the building. It should also be noted that after the Bhuj earthquake, Indian Standard IS: 1893 was revised and Chennai city was upgraded from zone II to zone III which leads to a substantial increase of the design ground motion parameters. Hence, this project presents an exploratory analysis of the seismic performance of multi-storey buildings system built in the specified area with a comparative study of the structures under past major earthquakes.Computer modeling is undertaken using Ansys is a multi-purpose software which enables to run and simulate tests or working conditions. It also helps in determining and improving weak points, computing by 3D simulations in virtual environment.

Index Terms— Auditorium, Analysis, Ansys, Earthquake, Seismic, Finite Element Analysis, Static Analysis —————————— ——————————

1 INTRODUCTION n auditorium is a room built to enable the Stress analysis one of the engineering discipline helps in de- Aaudience to hear and watch performances at termining stress in materials and structures that are subjected venues such as theatres. Generally, an auditorium to static or dynamic forces. has an increasing sloped-styled seating, So as to The aim of this analysis is to determine the collection of el- allow the audience at the back of the auditorium ements, which is also referred as a structure, can safely with- to see the stage without any disturbances. The stand the specified forces. This can be achieved when the de- structural design of an auditorium should be a termined stress from the applied forces are less than the ulti- sloped foundation so as to follow the seating mate tensile strength and the ultimate compressive strength layout. Seismic analysis of an auditorium is done the material is known to be able to withstand, inspite of that a using Ansys and various seismic modes and data factor of safety is applied in design. are collected. The member with the highest The factor of safety is one of the important design require- deflection is pointed out and strenghtening ments for any structure based on uncertainty in loads, materi- methods can be carried out in the next project. al strength (yield and ultimate), and consequences of failure. IJSERThe factor of safety is to prevent detrimental deformations and the factor of safety on ultimate strength is to prevent collapse. 2 OBJECTIVE OF THE PROJECT The factor of safety is used to calculate the maximum allowa- x To create a 3-D finite element model ble stress. Factor of Safety = Ultimate Tensile Strength/Maximum al- x Analyse the element using Static structural analysis, lowable stress Modal analysis and Response spectrum analysis When performing stress analysis, a factor of safety is calcu- lated to compare with the required factor of safety. The factor x Find out the member with maximum displacement of safety is a design requirement given to the stress analyst. The Analyst calculates the design factor. Margin of safety is due to seismic activity. another way to express the design factor. Design Factor = Ultimate Tensile Strength / Maximum Cal- culated Tensile Stress. A key part of analysis involves deter- 3 METHODOLOGY mining the type of loads acting on a structure, including ten- 3.1 Finite Element Program sion, compression, shear, torsion, bending, or combinations of such loads. The ANSYS program is a computer program for Fi- nite element analysis and design. Also used to find 3.3 Problem Definition out how a given design works under operating conditions. It has its own integrate pre and post processor. The finite element method is a numerical method for solv- Ansys program can be used in all disciplines of engi- ing problems of engineering and mathematical physics. It is neering-structural, mechanical, electrical, electromag- useful for problems with complicated geometries, loadings, netic, electronic, thermal, and fluid. and material properties where analytical solutions cannot be 3.2 Basic Concepts in FEA obtained.

IJSER © 2014 http://www.ijser.org International Journal of Scientific & Engineering Research, Volume 5, Issue 4, April-2014 1124 ISSN 2229-5518 FEA is a technique that discretizes a given physical or elements. But structural dynamics analysis tetrahedral mesh is mathematical problem into smaller fundamental parts called sufficient. Structural analysis using Finite Element Method elements. An analysis of each element is conducted. A solution gives a preliminary assessment of dynamic behavior of me- to the problem as a whole is obtained by assembling the indi- chanical structures in order to establish the guidelines for de- vidual solutions of the elements. Complex problems can be signing the experiment. The main objective of this study was tackled by dividing the problem into smaller and simpler to develop a methodology of seismic analysis of electronic problems that can be solved using existing mathematical tools. cabinets using ANSYS. Generally has two approaches i.e. transient analysis and response spectrum analysis are adopted for the seismic analysis in ANSYS. 3.4 Steps in Finite Element Modeling

1. Discretize and Select Element Types 5 MESHING 2. Select a Displacement Function 3. Define the Stress/Strain Relationships Meshing is used in a Workbench is to provide robust, ease 4. Derive the Element Stiffness Matrix and Equations in the use of meshing. These tools are highly automated and it 5. Assemble the Element Equations to obtain the Global has a moderate to high degree of user control. To carry out a Equations finite element analysis, the model must be divided into a 6. Solve for the Unknown Displacements number of small pieces and those pieces are known as finite 7. Solve for the Element Strains and Stresses elements. After the model has been divided into a number of 8. Interpret the Results. discrete parts, Finite Element Analysis can be described as a discretization technique. 3.5 Finite Element Meshing of Auditorium If the system we investigate is one-dimensional in nature, we may have to use line elements to represent our geometry Grid generation is the first step of analysis. Grid generation and carry out our analysis. If the system is two-dimensional, usually requires simplification and idealization of the design then a 2D mesh is required If the system is a complex and 3D model. This requirement is the most cumbersome aspect of representation of the continuum, then we use a 3D mesh. grid generation process. Therefore, the analysis model is often rebuilt from scratch, based upon the judgment of skilled ana- 5.1 Mesh Requirements lysts in removing details from the design, and duplicating The Finite Element Method (FEM) has certain requirements much of the work in creating the geometry. Often, integrated on a mesh: tools are interactive and require the design engineer to pro- x The mesh must be valid, (no holes, self-intersections, vide complex input. or faces joined at two or more edges). The geometrical question in a finite-element analysis x The mesh must conform to the boundary of the do- is represented by collection of finite elements used and is main. This is an obvious requirement, but some known as mesh. Creating theIJSER mesh is often the most difficult schemes such as a Delaunay triangulation may not part of finite element modelling. As a result, the grid genera- satisfy this condition. tion process is not yet a ‘push button" process; it is the most x The density of the mesh must be controllable, to allow labor- intensive and time-consuming aspect of the computa- trade-off between accuracy and solution time. tional structural dynamics. It takes too many man-hours and x The grid density will vary depending on local accura- calendar days, and it requires a grid specialist. Mesh genera- cy requirements, but any variations must be smooth tion could be performed graphically, drawing lines on a com- to reduce or eliminate numerical diffusion/refraction puter to form elements. Techniques such as extruding a shell effects. mesh to create a solid mesh were developed for creating com- x There are some requirements on the shape of ele- plex geometric models. With use of solid modelling CAD pro- ments. In general, the elements should as equiangular grams, the geometry to be used in finite element analysis al- as possible in equilateral triangles & regular tetrahe- ready exists in some format. This geometry can be used for dral. Highly distorted elements (long, thin triangles, simulation, only if the programs being used have the interface squashed tetrahedral) can lead to numerical stability capabilities. Once we have creared the geometry in the system, problems caused by round-off errors. This require- the finite element programs create some type of automatic ment is modified for boundary layers, where highly meshing. In beam elements it is the process of breaking up stretched elements are desired and facilitated in the bigger line entities into smaller line entities. In 2D elements, FEM formulation. The min-max-angle property is still flat surfaces must be broken into the elements having three or required in this case. four sides. In shell elements, 3D surfaces must be equally di- Figure below shows the FEA Model with Meshing which vided into the shell elements. In solid elements, a particular includes 320 columns and 494 beams. volume must be sectioned into elements.Automatic meshing capabilities directs the user place the elements. Most automatic mashers create tetrahedral elements in solid volumes. Tet- rahedral elements can be less in accuracy compared to brick

IJSER © 2014 http://www.ijser.org International Journal of Scientific & Engineering Research, Volume 5, Issue 4, April-2014 1125 ISSN 2229-5518 ditions on a structure. A static analysis includes steady inertia loads and time-varying loads that can be accounted as static equivalent loads. Static analysis is used to determine the displacements, stresses, strains, and forces in structures or components. These are the kinds of loading that can be applied in a static analysis : x Externally applied forces and pressures x Steady-state inertial forces (gravity or rotational velocity) x Imposed (non-zero) displacements x Temperatures (for thermal strain) x Fluences (for nuclear swelling)

6.1 Overview Of Steps in a Static Analysis The procedure for a static analysis consists of three main steps: x Building the model. x Applyong loads and obtaining the solution. x Reviewing the results.

IJSERFixed Support BC’s FEA Model with Meshing-320 columns and 494 beams

Meshing Top View

6 STATIC STRUCTURAL ANALYSIS Static analysis calculates the effects of steady loading con- IJSER © 2014 http://www.ijser.org International Journal of Scientific & Engineering Research, Volume 5, Issue 4, April-2014 1126 ISSN 2229-5518

Maximum Displacement 5mm

Total Bending Moment

Maximum Displacement 5mm

Displacement Contours

IJSERMaximum Combined Stress

Maximum Displacement 5mm

Displacement Contours-Top View

Torsional Moment

6.2 Modal Analysis

Natural Frequencies of Indoor Stadium

Mode-1

The first mode of the auditorium is rotating about an axis parallel to the x-axis in the E-W direction and the building swings in the N-S direction (Figure 6.11). The second and third modes are both twisting, in clockwise and counter- Mode-5 clockwise, respectively (Figure 6.12 and 6.13). The fourth mode is bending in the N-S direction (Figure 6.14). The last mode shows severe vertical motion at the northwest part of the auditorium and some bending (Figure 6.16).

Mode-2 IJSERMode-6

Mode-3 Mode-7

Large model Small model Mode extraction Long transient љ љ Mode shapes Response spectrum

Full solution Combined solution Slow, accurate Fast, approximate

Mode-8 Response Spectrum Analysis

9.000 8.000 7.000 6.000 5.000 4.000 3.000 ceeainm/s2 Acceleration 2.000 1.000 0.000 0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00 Mode-9 Frequency Hz IJSERSeismic Load

Mode-10 Deformation -X

6.3 Response Spectrum Analysis It uses the results of a modal analysis with a known spectrum to calculate displacements and stresses in the model. The spectrum is a graph of “spectral value” versus “frequency” that captures the intensity and frequency content of time- history loads.

IJSER © 2014 http://www.ijser.org International Journal of Scientific & Engineering Research, Volume 5, Issue 4, April-2014 1129 ISSN 2229-5518 Deformation –Y Civil Engineering Department, Bharath University, Chennai. I am grateful to the support and assistance provided by the team of talented and dedicated technical staff.

REFERENCES [1] Iqbal, A., S. Pampanin, A. Buchanan and A. Palermo. (2007) “Improved Seismic Performance of LVL Post-tensioned Walls Coupled with UFP devices” ." ACI Structural Journal, 62(2),348-352 [2] Newcombe, M. P., S. Pampanin, A.Buchanan and A. Pa- lermo 2008. “Section Analysis and Cyclic Behavior of Post- Tensioned Jointed Ductile Connections for Multi-Story Timber Buildings”, Journal of Earthquake Engineering Vol. 12(1): 83–110. Deformation -Z [3] Durrani A. J. and J. K. Wight (1985). "Behavior of Interior Beam-to-Column Connections Under Earthquake-Type Spectrum analysis yielded a lot of information. For the excita- Loading." ACI Structural Journal, 82(3),343-349. tion, there are three displacement response values at each [4] Pampanin, S., C. Christopoulos and M. J. Nigel Priestley node: translational displacements in the x, y and z direction, 2003. “Performance-Based Seismic Response of Frame Struc- rotations about the x, y and z axis, and total displacement and tures Including Residual Deformations. Part II: Multi-Degree of rotation. The same can be said about the acceleration. There- Freedom Systems” Journal of Earthquake Engineering Vol. fore, a total of 3 displacement graphs can be generated. In 7(1): 119-14 addition, vector graphs can also be created. [5] Carr A. J., (June, 1994). "Dynamic Analysis of Structures." Bulletin, New Zealand National Society for Earthquake Engi- neering, 27(2), 129-146. 7 CONCLUSION [6] Priestley M.J.N. and M.J.Kowalaky, (December, 2000). "Di- A 3-D finite element model was built and analyzed in the rect Displacement-Based seismic Design of Concrete Build- study. The model is based on the actual dimensions from the ings."Bulletin, New Zealand National Society for Earthquake blueprint and includes all structural components. Static and Engineering, 33(4), 421-444. Modal and spectrum analyses were performed with the FE package, ANSYS. The fundamental frequency obtained from the modal analysis compares well with the empirical value. Displacement, acceleration IJSERand stress distributions are generated from spectrum analysis with the response spectrum. It is suggested from the analyses that the most sensitive areas for the accelerate meters to pick up structural motions are the top level and the northwest part of the building. .

ACKNOWLEDGMENT My foremost gratitude goes to all that have contributed in the achievement of this study.I am Grateful to the Honourable Chancellor, Dr.J.Sundeep Anand, Bharath University, Chen- nai.

I am Grateful to Dr.v. Tamizharasan, Head Of the Depart- ment, Civil Engineering, Bharath University, Chennai. I am deeply indebted to my supervisor, Professor S. Aravindan, Assistant professor, Civil Engineering, Bharath University, Chennai.

I am sincerely grateful to Library of Structural Engineering Research Centre, Taramani, Chennai, for their support in providing me with Journals.